Quote:
The Challenge is such a unique opportunity for us as teachers to challenge and channel our students into a world of scientific inquiry and academics that goes beyond high school. - Beckey, Melrose High School

Development of More Efficient Fusion Reactors Through Computer Modeling

Team: 3

School: Albuquerque Academy

Area of Science: Nuclear Physics

Interim: Team #3
Che Olavarria-Gallegos & Jorge Antonio Perez
Mr. Mims
Supercomputing Challenge Proposal
10 December 2014
Supercomputing Challenge 2015: Interim Report
Problem Statement:
Producing the conditions necessary for nuclear fusion in current reactor designs requires using more energy than the process of fusion releases. This is due to the level of energy required to overcome the electrostatic repulsion between nuclei when bringing them sufficiently close together to fuse.
Overcoming this obstacle, thereby allowing power production through fusion, will provide humanity with a near-limitless source of clean energy. Current costs of building reactors large enough to create fusion using current designs make the technology prohibitively expensive, however as demonstrated by Lockheed Martin’s recent, but as-of-yet incomplete, breakthrough, finding more efficient, more “optimal” designs for fusion reactors could eliminate this problem.
Problem solution:
The first step to solving the problem is to develop a program to simulate the behavior of protons (and possibly electrons) under the influence of electric and magnetic fields. To make the simulator it looks like we will need six different tasks to be accomplished. The first two that need to be done are to calculate the magnetic and electric fields created by the reactor at a given point. The third thing that we need to create is a Barnes-Hut tree for the particles in the algorithm. The fourth function we need is one that will approximate the electric fields exerted by the plasma itself using the Barnes-Hut tree. Fifthly we need to calculate the new position and velocity of the particle based on the force exerted on the particle and the mass of the particle. For this we will assume that the force remains constant over a small time interval. The last five steps will be looped until the simulation is finished. The last function we need is one to calculate the efficiency of the reactor. If we can write all these functions then we should have our simulator.
The next step to solving this problem is to make a genetic algorithm to test different parameters of the reactor. The genetic algorithm will initially have to test hundreds of simulations using random parameters in a range we provide. The most efficient of these will “live,” becoming the starting point for the next generation. As generations progress, the range of values that parameters can take narrows, eventually converging on a design for a reactor with near-optimal fitness. If the range in which the computer is searching for new values falls below the expected level of precision with which a reactor could be constructed (such as when the computer starts to compare models differing in size on less than the scale of a millimeter), or if varying the parameters ceases to make a significant improvement to the efficiency of the reactor, then the search is “complete”.
The last step to benchmark test our reactor and genetic algorithm combination. We have to make sure that the simulation good. The simulator does not necessarily have to be accurate as long as it captures the trends. We can use the benchmark testing software to get a pretty accurate estimate of the efficiency of the reactor with the final parameters. For the benchmark tests we plan to enlist the help of professionals and high quality software.
Progress to date:
The genetic algorithm: we have completed a genetic algorithm which will find the set of floating-point values which optimizes the output of any function which takes the set of floating-point values as an input. To put it simply, the genetic algorithm will find n values in a given range which maximize the output of a given function.
The Barnes-Hut algorithm: we have completed an implementation of the Barnes-Hut algorithm that is capable of handling plasmas. Unlike the conventional Barnes-Hut algorithm, this modified version has two trees: one for positively charged particles and one for negatively charged particles. Particles then calculate the electric field produced by particles in each tree separately at their current location, and then sum the results to find the actual electric field exerted by the plasma. Our implementation attempts to ensure a great degree of efficiency; as a result, it avoids the use of recursive functions which call themselves. Currently, the slowest component is the method calculating the force on a particle: the construction AND calculation of mass distribution of a 3-dimensional tree is approximately 5-10 times faster. Memory allocation is not a slowdown, as the program stores unused nodes in a “node buffer”.
Calculation of position and velocity: we have been able to complete methods capable of calculating the new location and velocity of a particle using a time-step model. This part is not a significant concern.
Calculation of the electric field of a uniformly charged cylinder: this part needs to be made more efficient. We are currently treating the cylinder as a collection of charged points in space; calculations of this type could be vastly improved by various methods of integration. Integrating by adding together the areas of thin trapezoids seems most promising.
Calculation of the magnetic field of a wire: we have yet to implement this.
We still need to implement an algorithm that determines “fitness” or “efficiency” of a reactor, and an algorithm that calculates the charge distribution over a charged surface.
Concern: if we simulate a charged plasma, electrons would be moving ~40 times faster than the protons in the plasma, thus approaching relativistic speeds. The simulation does not currently account for special relativity.
Expected Results:
This project can run into two ruts. The first is highly inaccurate simulations: if the simulated plasma doesn’t behave accurately, then the behavior of a simulated reactor could vary greatly from the behavior of an actual reactor and any designs evaluated and discovered by the genetic algorithm are essentially worthless. The second is that the design doesn’t matter much, so the genetic algorithm is not much of a benefit because the most efficient reactor it discovers still isn’t efficient enough to be useful.
If the genetic algorithm provides useful designs, then even if the simulations lack accuracy, we will have demonstrated the potential for methods such as genetic algorithms to be used to solve this sort of problem.
We hope, however, that the simulations are also accurate: in such a case, if the genetic algorithm proves to be useful, then it is possible we could come close to solving the problem of fusion power, provided the energy from fusion can be extracted in a useful way. However, there are a number of issues: special relativity could have a significant effect (and one which we fail to account for). Even if the simulations themselves accurately model the behavior of the plasma, the calculated efficiency for a design could be inaccurate or imprecise. As a result, any designs discovered by the genetic algorithm may not even be close to optimal.
“Energy for Future Centuries”, retrieved December 10, 2014 http://www.agci.org/dB/PDFs/03S2_MMauel_SafeFusion%3F.pdf